Short Notes - Work and Energy
All living things need food for energy to survive and to do activities such as playing, running, hunting or defending themselves. Machines, such as cars or tools, also require a source of energy (for example, fuel or electricity) to perform work. In physics, the ideas of work, energy and power describe how forces cause motion, how that motion stores or uses energy, and how quickly energy is transferred.
What is Work?
Work is done when a force produces motion of a body in the direction of the force. Work done in moving a body is equal to the product of the force exerted on the body and the distance moved by the body in the direction of the force.
- Mathematical expression: W = F × s, where F is the component of force along the direction of displacement and s is the displacement.
- Physical nature: Work is a scalar quantity; it has magnitude only, not direction.
- SI unit: joule (J). One joule is the work done when a force of 1 newton displaces an object through 1 metre along the line of action of the force.
- Possible signs of work: Work done by a force can be positive, negative or zero depending on the relative directions of force and displacement.
- Positive work: When the force has a component in the same direction as the displacement, the work done is positive.
- Negative work: When the force has a component opposite to the displacement, the work done is negative.
- Zero work: When the force is perpendicular to the displacement, the work done by that force is zero.
(a) Positive work - example and formula
If the displacement is in the direction of the force, then W = F × s.
(b) Negative work - example and formula
If the displacement is opposite to the force, then W = -F × s.
(c) Zero work - example and explanation
If the displacement is perpendicular to the force, the work done by that force is zero because the component of force along displacement is zero.
What is Energy?
Energy is the capacity to do work. The amount of energy a body possesses equals the maximum work it can do when that energy is released.
- Energy is a scalar quantity.
- SI unit of energy is the joule (J). 1 kJ = 1000 J.
- Common forms of energy: kinetic energy, potential energy, chemical energy, heat (thermal) energy, light energy, sound energy, electrical energy and nuclear energy.
Kinetic Energy
Kinetic energy is the energy possessed by a body due to its motion. For a given mass, kinetic energy increases with speed. The kinetic energy of a body equals the work done on it to bring it from rest to its present speed.
Derivation of kinetic energy formula (for constant force):
Let an object of mass m initially move with velocity u. A constant force F acts on it, producing acceleration a, and displacing it through distance s so that its final velocity becomes v.
Work done by the force is
W = F × s
The kinematic relation between velocities, acceleration and displacement is
v² - u² = 2 a s
Newton's second law gives
F = m a
Substitute F = ma and s from the kinematic relation into the expression for work:
W = F × s = m a × s
Using s = (v² - u²) / (2a) gives
W = m a × (v² - u²) / (2 a)
Therefore
W = 1/2 m (v² - u²)
Thus the work done by the net force equals the change in kinetic energy. If the object starts from rest (u = 0), the kinetic energy Ek is
Ek = 1/2 m v²
Potential Energy
Potential energy is the energy possessed by a body due to its position in a force field or due to its configuration (shape). The most common example is gravitational potential energy near Earth's surface.
Gravitational potential energy (GPE): When an object of mass m is raised through a vertical height h in Earth's gravitational field, work is done against gravity. The energy gained by the object is the gravitational potential energy.
Derivation of GPE near Earth's surface:
Consider a body of mass m raised vertically through height h. The weight (force due to gravity) acting downward is mg.
Work done against gravity = force × displacement
W = mg × h
So the increase in gravitational potential energy is
PE = m g h
- Path independence: For conservative forces like gravity, the work done in moving a body between two vertical positions depends only on the change in height, not on the path taken. Therefore GPE change from A to B depends only on difference in heights.
- Mechanical energy: The sum of kinetic energy and potential energy of a system is called its mechanical energy.
Note: Energy cannot be created or destroyed; it can only be transformed from one form to another. The total energy of an isolated system remains constant.
Consider a body of mass m raised to height h (position A). At A the body is momentarily at rest, so its potential energy is maximum and kinetic energy is zero. As the body falls, height decreases so potential energy decreases and speed increases so kinetic energy increases. Just before reaching ground level (height = 0), potential energy is minimum and kinetic energy is maximum. The loss in potential energy equals the gain in kinetic energy (neglecting non-conservative forces such as air resistance).
Law of Conservation of Energy
The Law of Conservation of Energy states that energy can neither be created nor destroyed; it can only change from one form to another. The total energy of an isolated system remains constant. This principle governs many physical, chemical and biological processes.
Example: A cyclist moving up a hill has kinetic energy at the bottom and, as the cyclist climbs, kinetic energy is converted into gravitational potential energy. At the top of the hill most of the energy is in the form of potential energy. Neglecting friction and air resistance, the total mechanical energy remains the same at corresponding points.
What is Power?
Power is the rate at which work is done or the rate at which energy is transferred.
- Mathematical definition: Power P = W / t, where W is the work done (or energy transferred) in time t.
- SI unit: watt (W). One watt equals one joule per second (1 W = 1 J s⁻¹).
- The unit is named after the engineer James Watt.
- Kilowatt: For larger power quantities, 1 kilowatt (kW) = 1000 W. Many household appliances are rated in watts or kilowatts.
- Instantaneous and average power: Instantaneous power is the power at a particular instant; average power over an interval is total energy transferred divided by the total time taken.
- Average power formula: Pavg = ΔE / Δt, where ΔE is the energy transferred in time interval Δt.
Additional notes and simple applications
- When multiple forces act on a body, the work done by the net force equals the change in kinetic energy (work-energy theorem).
- Friction and other non-conservative forces convert mechanical energy into thermal energy; in such cases mechanical energy is not conserved, but total energy (including heat) still obeys conservation.
- Power ratings of motors and heaters tell how quickly they can do work or transfer energy. For example, a 1000 W heater transfers 1000 J of heat each second when operating at full power.
- Units conversion reminder: 1 J = 1 N × 1 m; 1 kJ = 1000 J; 1 Wh = 3600 J (useful when comparing electrical energy in common units).
Key formulas (for quick reference):
- Work: W = F × s
- Kinetic energy: Ek = 1/2 m v²
- Gravitational potential energy: PE = mgh
- Power: P = W / t
FAQs on Short Notes - Work and Energy
| 1. What exactly is work in physics and how is it different from effort? |  |
| 2. How do I calculate work done when force and displacement aren't in the same direction? | |
| 3. What's the relationship between work and energy, and why does it matter for my exams? | |
| 4. Can work be negative, and what does that actually mean in real situations? | |
| 5. How are joules and watts connected, and which one measures what in energy calculations? | |
